Image Classification with Convolutional Neural Networks
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Image Classification with Convolutional Neural Networks
In this project, I implemented a Convolutional Neural Network (CNN) for image classification using PyTorch. The model was trained on the CIFAR-10 dataset and achieved an accuracy of 85% on the test set.
Project Overview
- Dataset: CIFAR-10
- Framework: PyTorch
- Model Architecture: Custom CNN with 3 convolutional layers and 2 fully connected layers
- Training: 50 epochs using Adam optimizer
Key Learnings
- Importance of data augmentation in improving model generalization
- Impact of learning rate scheduling on training stability
- Techniques for visualizing and interpreting CNN features
Mathematical Formulation
The convolution operation in a CNN can be expressed as:
\[(f * g)(t) = \int_{-\infty}^{\infty} f(\tau) g(t - \tau) d\tau\]For a 2D image $I$ and a kernel $K$, the discrete convolution is:
\[(I * K)(i, j) = \sum_{m} \sum_{n} I(m, n)K(i-m, j-n)\]The activation function we used is the Rectified Linear Unit (ReLU):
\[f(x) = \max(0, x)\]Loss Function
We used the cross-entropy loss function, defined as:
\[L = -\sum_{i} y_i \log(\hat{y}_i)\]where $y_i$ is the true label and $\hat{y}_i$ is the predicted probability for class $i$.
Future Work
- Implement transfer learning using pre-trained models like ResNet
- Explore more advanced architectures like Inception or DenseNet
- Apply the model to a real-world image classification task
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